Details

Time bar (total: 35.4s)

sample152.0ms

Algorithm
intervals
Results
51.0ms256×body80valid
34.0ms280×body80nan

simplify1.2s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02833
15033
210633
337333
4149733
done500133

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.5b

localize44.0ms

Local error

Found 4 expressions with local error:

0.3b
(* z (sqrt (+ t a)))
0.3b
(/ 2.0 (* t 3.0))
2.2b
(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
5.9b
(/ (* z (sqrt (+ t a))) t)

rewrite127.0ms

Algorithm
rewrite-expression-head
Rules
20×frac-sub
16×add-exp-log add-cbrt-cube
15×add-sqr-sqrt
13×*-un-lft-identity
11×add-cube-cbrt
9×flip3-- flip--
8×frac-times associate-*r/
7×associate-*r*
6×pow1 times-frac associate--r+ add-log-exp
5×flip3-+ sqrt-prod flip-+
4×cbrt-undiv sqrt-div div-exp associate-/r* associate-/l*
3×distribute-rgt-in sub-neg distribute-lft-in associate-*l* prod-exp cbrt-unprod
2×frac-2neg associate-*l/ associate--l+ clear-num div-inv associate-/l/ unswap-sqr
1×diff-log pow-prod-down *-commutative distribute-lft-out
Counts
4 → 101
Calls
4 calls:
41.0ms
(* z (sqrt (+ t a)))
10.0ms
(/ 2.0 (* t 3.0))
53.0ms
(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
16.0ms
(/ (* z (sqrt (+ t a))) t)

series429.0ms

Counts
4 → 12
Calls
4 calls:
95.0ms
(* z (sqrt (+ t a)))
18.0ms
(/ 2.0 (* t 3.0))
225.0ms
(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
91.0ms
(/ (* z (sqrt (+ t a))) t)

simplify2.2s

Counts
113 → 113
Iterations

Useful iterations: 2 (843.0ms)

IterNodesCost
03442616
110152408
243572288
done50002288

prune1.0s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.3b

localize37.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (- b c) (- (+ a (/ 5.0 6.0)) (/ 0.6666666666666666 t)))
0.3b
(* z (sqrt (+ t a)))
2.2b
(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 0.6666666666666666 t))))
5.9b
(/ (* z (sqrt (+ t a))) t)

rewrite412.0ms

Algorithm
rewrite-expression-head
Rules
26×frac-sub
24×add-sqr-sqrt
20×*-un-lft-identity
17×flip3-- flip--
16×frac-times
14×associate-*r*
13×add-exp-log add-cbrt-cube
12×associate-*r/
11×add-cube-cbrt
8×pow1 flip3-+ associate-*l* flip-+
6×distribute-rgt-in distribute-lft-in associate--r+ add-log-exp
5×sub-neg sqrt-prod
4×times-frac sqrt-div associate-*l/ associate--l+
3×prod-exp associate-/r* cbrt-unprod distribute-lft-out-- difference-of-squares unswap-sqr
2×cbrt-undiv div-exp pow-prod-down *-commutative associate-/l/ distribute-lft-out
1×frac-2neg diff-log clear-num div-inv associate-/l*
Counts
4 → 124
Calls
4 calls:
293.0ms
(* (- b c) (- (+ a (/ 5.0 6.0)) (/ 0.6666666666666666 t)))
36.0ms
(* z (sqrt (+ t a)))
60.0ms
(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 0.6666666666666666 t))))
17.0ms
(/ (* z (sqrt (+ t a))) t)

series504.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(* (- b c) (- (+ a (/ 5.0 6.0)) (/ 0.6666666666666666 t)))
71.0ms
(* z (sqrt (+ t a)))
243.0ms
(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 0.6666666666666666 t))))
120.0ms
(/ (* z (sqrt (+ t a))) t)

simplify2.2s

Counts
136 → 136
Iterations

Useful iterations: 2 (973.0ms)

IterNodesCost
03503379
110113127
243382999
done50022999

prune1.1s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.3b

localize107.0ms

Local error

Found 4 expressions with local error:

2.8b
(* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0))
3.4b
(* t (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0))))
6.8b
(- (* (* z (sqrt (+ t a))) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* t (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0)))))
26.7b
(/ (- (* (* z (sqrt (+ t a))) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* t (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0))))) (* t (* (- a (/ 5.0 6.0)) (* t 3.0))))

rewrite2.4s

Algorithm
rewrite-expression-head
Rules
766×associate-*l/
764×associate-*r/
524×frac-sub
498×flip3-- flip--
364×frac-times
240×sqrt-div
162×associate-/l/
120×flip3-+ flip-+
28×add-exp-log add-cbrt-cube
16×distribute-rgt-in distribute-lft-in
14×pow1
12×prod-exp cbrt-unprod
9×sub-neg
8×add-sqr-sqrt add-cube-cbrt *-un-lft-identity associate--r+
7×associate-*l*
6×pow-prod-down add-log-exp
4×cbrt-undiv div-exp
3×times-frac associate-/l*
2×associate-*r* associate-/r/ *-commutative
1×frac-2neg diff-log div-sub clear-num associate-/r* div-inv difference-of-squares
Counts
4 → 437
Calls
4 calls:
56.0ms
(* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0))
463.0ms
(* t (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0))))
678.0ms
(- (* (* z (sqrt (+ t a))) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* t (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0)))))
1.1s
(/ (- (* (* z (sqrt (+ t a))) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* t (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0))))) (* t (* (- a (/ 5.0 6.0)) (* t 3.0))))

series2.6s

Counts
4 → 12
Calls
4 calls:
64.0ms
(* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0))
323.0ms
(* t (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0))))
972.0ms
(- (* (* z (sqrt (+ t a))) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* t (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0)))))
1.3s
(/ (- (* (* z (sqrt (+ t a))) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* t (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0))))) (* t (* (- a (/ 5.0 6.0)) (* t 3.0))))

simplify2.7s

Counts
449 → 449
Iterations

Useful iterations: done (2.7s)

IterNodesCost
0115350141
1461544541
done500043557

prune9.6s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize53.0ms

Local error

Found 4 expressions with local error:

0.0b
(* y (exp (* 2.0 (- (+ (* 1.0 (* a c)) (* 0.8333333333333334 c)) (* 1.0 (* a b))))))
0.0b
(+ (* 1.0 (* a c)) (* 0.8333333333333334 c))
0.0b
(/ x (+ x (* y (exp (* 2.0 (- (+ (* 1.0 (* a c)) (* 0.8333333333333334 c)) (* 1.0 (* a b))))))))
1.8b
(- (+ (* 1.0 (* a c)) (* 0.8333333333333334 c)) (* 1.0 (* a b)))

rewrite354.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
14×add-cube-cbrt *-un-lft-identity
11×add-log-exp
9×times-frac associate-*r*
8×add-cbrt-cube
7×add-exp-log
6×pow1 exp-sum
3×distribute-rgt-in sub-neg distribute-lft-in associate-*l* associate--l+ associate-/r* associate-/l*
2×flip3-+ diff-log sum-log associate-/r/ flip-+
1×cbrt-undiv +-commutative flip3-- frac-2neg div-exp pow-prod-down prod-exp clear-num *-commutative flip-- cbrt-unprod div-inv unswap-sqr
Counts
4 → 78
Calls
4 calls:
115.0ms
(* y (exp (* 2.0 (- (+ (* 1.0 (* a c)) (* 0.8333333333333334 c)) (* 1.0 (* a b))))))
34.0ms
(+ (* 1.0 (* a c)) (* 0.8333333333333334 c))
19.0ms
(/ x (+ x (* y (exp (* 2.0 (- (+ (* 1.0 (* a c)) (* 0.8333333333333334 c)) (* 1.0 (* a b))))))))
181.0ms
(- (+ (* 1.0 (* a c)) (* 0.8333333333333334 c)) (* 1.0 (* a b)))

series516.0ms

Counts
4 → 12
Calls
4 calls:
147.0ms
(* y (exp (* 2.0 (- (+ (* 1.0 (* a c)) (* 0.8333333333333334 c)) (* 1.0 (* a b))))))
74.0ms
(+ (* 1.0 (* a c)) (* 0.8333333333333334 c))
223.0ms
(/ x (+ x (* y (exp (* 2.0 (- (+ (* 1.0 (* a c)) (* 0.8333333333333334 c)) (* 1.0 (* a b))))))))
71.0ms
(- (+ (* 1.0 (* a c)) (* 0.8333333333333334 c)) (* 1.0 (* a b)))

simplify1.6s

Counts
90 → 90
Iterations

Useful iterations: done (1.6s)

IterNodesCost
01522307
13752220
212481840
done50011682

prune468.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes375.0ms

Accuracy

-7.3% (3.6b remaining)

Error of 4.0b against oracle of 0.4b and baseline of 3.7b

bsearch540.0ms

Steps
ItersRangePoint
9
2.5571904280608065e-113
1.1606791802233116e-106
3.585798647479515e-110
7
-8.64205799040136e-295
-3.387906247697725e-297
-5.86945893495286e-296

simplify22.0ms

Iterations

Useful iterations: 1 (14.0ms)

IterNodesCost
054137
175107
done75107

end0.0ms

sample4.6s

Algorithm
intervals
Results
1.7s8153×body80nan
1.4s8000×body80valid